1. Field of the Invention
The invention belongs to the technical field of information security (IS), especially relating to an asymmetric-computing type shared key establishing method suitable for cloud computing and IoT.
2. Description of the Related Art
To solve the problem that key management is complex in a symmetric cryptosystem, Diffie and Hellman brought forward the concept of “public-key cryptosystem” innovatively in 1976 and indicated that secret information can be transmitted in a public channel. Compared with symmetric cryptograph, encryption and decryption algorithm in the public-key cryptosystem tend to be complex and low-efficiency, and are therefore not suitable for encrypting mass data directly. Generally, a shared conversation key is established by utilizing the public key cryptographic technology (i.e., a shared key establishment protocol), and then the conversation key serves as a key of the symmetric cryptograph to encrypt plaintext.
The Diffie-Hellman Key Exchange protocol provided in 1976 opens up a new area in public key cryptography. The Diffie-Hellman Key Exchange protocol is based on the discrete logarithm problem, and characterized in that two parties are in the peering environment and computation is symmetric, namely computation of the two parties is identical. With continuous development of the IT industry, the applications of the key exchange method keep changing, and the original Diffie-Hellman type key exchange method cannot be appropriately used between server and terminal, and between server and mobile equipment on occasions as cloud computing and Internet of Things (IoT). The two parties have great difference in computing resources and capabilities, and thus, a shared key exchange protocol with asymmetric computation is needed.
At present, quantum computers have appeared. Further development of the quantum computer may be a grave threat to the Diffie-Hellman Key Exchange protocol. Many existing protocols, such as the MQV protocol that serves as the IEEE P1363 standard, are formed by improving the Diffie-Hellman Key Exchange protocol, and most of the existing protocols are based on discrete logarithm or elliptic-curve discrete logarithm and thus, incapable of resisting attacks from the quantum computer. A shared key exchange protocol that can resist the attack from the quantum computer is needed. Anshel et al. brought forward a shared key protocol based on common non-commutative groups in 1999 and a double-party shared key exchange protocol in 2001; however, both the protocols are proved to be insecure. Ko et al. put forward the called Diffie-Hellman type conjugate problem (DHCP) in CRYPTO 2000, and further brought forward a Diffie-Hellman type bilateral shared key exchange protocol; however, Cheon et al. suggested a polynomial time algorithm to solve the DHCP in 2003, and Myasnikon et al. even provided a more effective solution. In PQCrypto 2010, Boucher et al. proposed another bilateral shared key exchange protocol which is based on special non-commutative multiplication polynomial, but the bilateral shared key exchange protocol by Boucher was challenged by Dubois and et al. later.